A Particle in a Square Well

Lu Yinji, Hou Xianhuai

I. Richard Lapidus

YI Qi-shun

The demonstration device of the particle's probability density in one-dimensional infinite square well is design.Standing wave image of particle's state function is used to demonstrate particle's probability density.The students can intuitively observe the law of particle's probability density at different places in one-dimensional infinite square well.

Tapan Kumar Das

Akira Tamura, Yohhei Tatsumi

Abstract In order to specify the uncertainty relation for a particle confined in a finite square well potential we derived the standard deviation of momentum Δ p and that of position Δ x . It is shown that Δ p has a peak as a function of the well width and both Δ x and Δ p ⋅ Δ x have a dip in contrast to the case of the particle confined in an infinite square well potential. We clarified that Δ p 0 ⋅ Δ x 0 of the particle occupying the ground state exists in the finite range as a function of the well width and the potential-barrier height, but a particle confined in an infinite square well potential has a constant Δ p 0 ⋅ Δ x 0 . In addition, we found that the values of Δ p n ⋅ Δ x n for excited states diverge in a certain range of well widths, where the energy level of the confined particle exceeds the potential barrier.

James M. Feagin